Two functions with C^n continuity over an interval:Which one's the smoothest?

According to the definition of Smooth function - Wikipedia, the free encyclopedia:

Functions that have derivatives of all orders are called **smooth**.

Suppose I've two different functions and of continuity over an interval . Because both of these functions has derivatives of all order these two functions are smooth.

What I like to know is which one of these two are smoothest?

Is it possible to kindly help me detect which function( or ) is the smoothest over the given interval?

Re: Two functions with C^n continuity over an interval:Which one's the smoothest?

How are **you** defining "smoothest"? Some times texts will say that if f is differentable "n" times and g is differentiable "m" times, with n> m, then f is "smoother" than g. But you are using "smooth" to mean what those texts would call "infinitely smooth" so that does not apply here.

Re: Two functions with C^n continuity over an interval:Which one's the smoothest?